I think you and I have very different ideas about what folk music is. Although I agree with your cultural understanding of the form, I think the bands mentioned are totally within the basic form of folk and have nothing to do with classical much at all. Secondly I think folk is firmly attached to a basic form of which more often than not shirks improvisation. It relies upon repeating basic melodies in minimal forms and with verse chrorus vocals laid over; in this sense Sol Invictus is totally closer to folk than classical (though it is, I acknowledge, without much of the cultural ideal you uphold). Finally, the idea that any of our respective cultures are alive enough to be producing worthy folk music is kind of funny. You said yourself the BS is folk for today.
For the purposes of this thread, let's first of all draw a distiction between folk and neo-folk.
IMO Sol Invictus, Death In June etc are quite boring musically, though the ideas and metaphors in the lyrics might make for an interesting listen now and then. Neo-folk projects (more often than not) use an easily digestible keyboard sound and electronic amplification which is has nothing in common with folk. Classical music relies on development, and pop usually drives the point home with a series of repetitive phrases- 'neo-folk' bridges the gap by using a 'classical' sound and pop structure. Needless to say, it falls between the two stools.
I admitted my broad generalisation when expressing opinion about Britney Spears. The majority of people goes for catchy tunes and slutty attitude, and it is only as a result of this utilitarian approach that I call BS 'folk for today's generation'.
As far as 'real' folk is concerned, I can only speak for myself. My native form of folk music includes improvisation as an important theme, both instrumentally and lyrically (indeed, the best songs feature two singers singing alternate verses, each trying to outdo the other in terms of storytelling and invention). And my culture is still alive enough to be producing worthy folk music on a frequent basis.